Question on Optics

Hi. "A biconvеx lеns has a focal length of 100mm. an object is placеd at distancеs of 150 mm and 75 mm from teh lens. Sketch a ray diagram to find the position of thе respective images. confirm these positiones via calculatinons.

So if am using 1 / f = 1 / s 1 + 1 / s 2 that would be (according to the diagram I've done) 1 / 75 + 1 / 75 which approximately equals 1 / 100 but what about 1 / 150 + 1 / 150 where that is 0.0067 which does not equal 1/100? Unless the diagram needs to be re drawn?

Think of the thin lens equation as 1/f = 1/do+ 1/di. Here do is the object distance, the distance between the object and the lens, and di is the image distance, the distance between the image and the lens. Use the equation to solve for di.

Also, it says "an object" so perhaps the 75 mm means 75 mm from the lens in one direction and 150 mm in the other direction? I've assumed the object has been placed at the two distances at one side of the lens.

You are supposed to figure out the location of the image for two cases: one where do = 75 mm and one where do = 150 mm. (The big difference is that in one case the object is inside the focal length, while in the other it is outside that length.)

Not really. To learn how to draw a ray diagram to calculate the image distance, read this: Ray Diagrams for Lenses.

Think of the thin lens equation as 1/f = 1/do+ 1/di. Here do is the object distance, the distance between the object and the lens, and di is the image distance, the distance between the image and the lens. Use the equation to solve for di.

You are supposed to figure out the location of the image for two cases: one where do = 75 mm and one where do = 150 mm. (The big difference is that in one case the object is inside the focal length, while in the other it is outside that length.)